Dota – Axe culling blades instant kill Damage

What does it mean that it is reduced by armor type but not by armor value?

When the wiki mentions armor type, its taking about the class of the armor on the target. I.e. hero armor, creep armor, building armor. So if great cleave hits a hero, it will still do only 75% of the regular damage due to the hero armor bonus, but the value of the hero armor will not affect damage done.

The fact that it goes through magic immunity it means that the damage is physical?

Not quite, there are some magical damage that can go through magic immunity (March of the Machines, for example.)

In this case, it probably does mean that its considered physical damage.

Yes, but armor doesn't work the way you think it does.

Armor acts like a damage multiplier, not addition or subtraction.

So a unit with -10 armor actually takes 46.1% more damage!

However, negative armor caps out at -20, which is equivalent to 71% more damage.

You also have to take into account of the type of armor. Remember that heroes have an innate resistance to most types of damage except from other heroes. Also, armor only works against physical damage.